ANDY RUINA: Bicycles are amazing that you can balance them. Somehow, you just, on two narrow wheels, you can keep them upright. And you can only keep them upright when they're moving.
And what's well-known about bicycle balance is that the major effect in bicycle balance is that steering is what gives you balance. If you lock the wheels of a bicycle so it can't steer, the angular momentum of the wheels contributes exactly nothing to bicycle stability. And it falls over when it's moving forwards, exactly the same way it falls over when it's stationary.
The amazing thing about bicycles is that they can balance themselves-- that somehow, a bicycle, if it's moving fast enough, and not too fast, will steer itself and balance.
I balance this. And I can balance this with my hands. And the basic mechanism of the balance, if you want to think about it, is that when it tips this way, I move my hand back under this way. When it tips this way, I move my hand back under this way. And this is the basic mechanism for bicycle balance.
So if you think of a bicycle rolling along, and it's falling this way, the way that a bicycle balances is that you steer it. And the steering doesn't do anything if a bicycle's not moving. But if a bicycle's moving forward, when you steer it, it moves the wheel sideways. And the net effect is-- I'll aim this at the camera-- is if the bicycle is leaning this way and you steer it, it pops the wheels underneath the top of the bicycle. So it's as if balancing the bicycle on my hand. And when the bicycle leans this way, you steering it brings the wheels back underneath. Steer it this way, it brings the wheels back underneath.
Now, the natural thing to think of is that it's something about a gyroscope. So that you know that when things spin fast, they somehow are rigid, because there's been a--
So here's a kid's gyroscope. And when it's spinning, think of it as a bicycle wheel spinning. It has a tendency to keep its alignment. So for example, it can balance. And you'd naturally think that a bicycle is stable because of the spinning. And, as I said, what we showed is that when you tied the handlebars and don't let it steer, this gyroscopic effect doesn't give any stability.
So what is it about the moving that gives the stability is that this spinning gyroscope has a squirrelly aspect, which you can feel when you hold a gyroscope. It's not just that it wants to keep this alignment. It's that when you try to turn it one way, the effect is to turn a different direction. So the net effect of that is that for a bicycle wheel, if a bicycle wheel is spinning-- so imagine this bicycle wheel is spinning like so-- that when the bicycle tips to one side, this wheel acts like a gyroscope. And the net effect of this tipping is that it causes the steering. And the result of that steering is that the bottom move to the side, and the wheels are brought back under the bicycle.
So that's one of the explanations for how bicycles can be self-stable. It's the gyroscope effect.
The other claim about bicycle self-stability-- how it can balance itself-- has to do with the casters. So this is a caster. And what a casters is is it's a wheel. But the wheel itself is mounted on something which has another axis. So where you see these, for example, is in the front wheels of grocery carts, and on the bottoms of chairs, and things like that. The job of this caster is that if you have some piece of furniture, a grocery cart, and it moves in one direction, the wheel follows around however you roll it.
Now, if you look at this thing, a bicycle in disguise is, itself, a caster. Because here we have a bearing for steering. And here we have a wheel which rolls on an axle. If you look at the bicycle, it's got this bearing for steering and a wheel that rolls on an axle. It's got different size to it.
Now, this is effect that the caster has, that it follows whichever way you move it, the reason it follows is because this wheel contact point is behind this pivoting or steering axis. And on a bicycle, this is a subtle bit of the geometry. But if you look at this steering axis, it comes down in a line like this. And it hits the floor about here, just under here. Whereas the wheel contact is back here.
So the calculations show that neither gyroscopic or trail effects were important. And then Jim Papadopoulous designed on pencil and paper a bicycle that did not have these effects. I then gave the challenge to my friend Arend Schwab in the Netherlands. And he, with his student Jodi Kooijman, built about one of these TMS-- two-mass-skate-- bicycles.
So what it is, it's a funny looking thing that looks, maybe, more like a scooter. But the idea is that it has no gyroscopic effect-- no spinning momentum effect-- because it has two front wheels and two back wheels. The second front wheel doesn't touch the ground. It just spins backwards to cancel the angular momentum. And the second back wheel spins backwards to cancel the angular momentum. And it doesn't have this caster effect, because it has the ground contact point actually slightly forward of the steering axis, instead of behind the steering axis as in a conventional bicycle.
And they pushed it. And it would balance itself. And they knocked it sideways a little bit. And it would pop back upright, just like the calculations said it should do.
It has to be that somehow, leaning causes steering. But there are various mechanical effects besides the gyroscopic effect and besides the caster effect where leaning can cause steering. And the mechanism that that bicycle has for being self-stable is that it has a mass on the front assembly which is forward of the steering axis. And it has a mass in the frame.
And when the bicycle falls, this one tends to fall faster, just like if your stick falls, and if the stick is shorter, it falls faster than the longer stick. So this front mass falls faster than the rear mass. But they're connected to each other by the steering axis. So in its attempt to fall faster, it causes steering. And that's what we think is the primary mechanism of stability of this TMS, this gyro-free and trail-free bicycle.
But there are other coupling effects that could contribute to self-stability of a bicycle. And they're in the equations. And they affect the self-stability, in principle, just as much as the gyro effect, the trail effect, or this gravity effect, which I just described.

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Most bicycles will stay upright as long as they're moving, even without a rider. Andy Ruina, Cornell professor of mechanics, describes recent research showing that the accepted wisdom about how bicycles balance themselves doesn't tell the whole story.